`Advances in Operations ResearchVolume 2010 (2010), Article ID 146042, 26 pagesdoi:10.1155/2010/146042`
Research Article

## A Production-Inventory Model for a Deteriorating Item Incorporating Learning Effect Using Genetic Algorithm

1Department of Mathematics, National Institute of Technology, Durgapur, West Bengal 713209, India
2Department of Computer Science, Prabhat Kumar College, Contai, Purba- Medinipur, West Bengal 721401, India

Received 20 November 2009; Revised 3 June 2010; Accepted 5 July 2010

Academic Editor: Frédéric Semet

Copyright © 2010 Debasis Das et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Demand for a seasonal product persists for a fixed period of time. Normally the “finite time horizon inventory control problems” are formulated for this type of demands. In reality, it is difficult to predict the end of a season precisely. It is thus represented as an uncertain variable and known as random planning horizon. In this paper, we present a production-inventory model for deteriorating items in an imprecise environment characterised by inflation and timed value of money and considering a constant demand. It is assumed that the time horizon of the business period is random in nature and follows exponential distribution with a known mean. Here, we considered the resultant effect of inflation and time value of money as both crisp and fuzzy. For crisp inflation effect, the total expected profit from the planning horizon is maximized using genetic algorithm (GA) to derive optimal decisions. This GA is developed using Roulette wheel selection, arithmetic crossover, and random mutation. On the other hand when the inflation effect is fuzzy, we can expect the profit to be fuzzy, too! As for the fuzzy objective, the optimistic or pessimistic return of the expected total profit is obtained using, respectively, a necessity or possibility measure of the fuzzy event. The GA we have developed uses fuzzy simulation to maximize the optimistic/pessimistic return in getting an optimal decision. We have provided some numerical examples and some sensitivity analyses to illustrate the model.